I get the sense from reading your question that not having a sense of what's actually useful to visitors and customers, and of what makes a good site vs a bad site, is probably what's hurting you the most.

Take a look at this thread, just posted, linking to an article in which Eric Enge and Matt Cutts discuss what makes a good quality site. I think it might be helpful to you, as I feel your questions are coming from an entirely wrong direction....

I don't suppose it's any use suggesting you might do it to be more natural. Oops. Wrong forum.

I see it like this: Sooner or later your visitors will have read every last page, including the technical specs for widgets that have been out of stock since 2007, and they will have to leave.* At that point they can either just wander off, or they can go where you want them to go-- retaining a vague memory that this second interesting site was recommended by that other interesting site.

To put it in more calculating terms: They go somewhere other than straight back to google. I believe this is generally held to be A Good Thing.

* Or, in my case: "If I read one more article about how to say 'leaf blower' in Inuktitut, I will go stark staring bonkers. That site about pastry cutters sounds interesting."

I would strongly recommend you try your own testing on this. It is almost completely ignored as a topic on this or any other forum, so any intelligence you gather would give you an edge over SEOs practicing third- or forth-hand advice.

I've done some testing several years ago and was unable to see any strong benefit from linking out. On the other hand, we couldn't see any harm either. When we link out we didn't see a loss in pagerank, a loss in traffic, or a loss in rankings. Given that it doesn't seem to hurt at all, users often find it helpful, and it might help, I do it. I recommend that you do it as well.

(In our tests we were linking out all the time, we just switched it from tracked redirects that googlebot couldn't follow because of robots.txt to clear dofollow links. So it is possible that Google know we were linking out all along from user analytics.)

It shouldn't affect your bounce rate, depending on what you mean by that.

You mention "weather". If you are not a meteorology, holiday booking, tourist info or similar, linking to weather will be counter-productive.

Nofollowing is a terrible idea. It's the kind of thing people do because they read it was a good idea. It isn't. It's a means of disincentivising UGC from spam linking, or to cite something dodgy: "I can't believe this article [linkbait.com]". Or to publish paid ads in a Google-compliant way.

If you are planning on using "popups" eek, then you might as well link to non-competing parallel sites. That will be of more value to your user, and... actually, do some testing.

Outbounds have tangible effect on the linking page, and indeed the linking site. You need to test on different targets, different contexts and a whole bunch of other things.

Frankly, I wouldn't expect that to work at all. Penguin is specifically targeted at webspam, so if that indeed is what hit your site, you've probably got much bigger fish to fry than wondering about having or not having any outbound links -- which, I would argue, would be a worthless quality signal anyway.

Should I put some nofollow links to "authority sites" to look more "natural"?

As Shaddows said, using nofollow here is not really a good idea. You're basically telling the search engines "See, I'm linking to authority sites," then turning around and saying "But I really don't want to editorially vouch for them so please don't pay attention the links."

I think the OP might be on to something. Here is what Matt Cutts said on the issue before Penguin:

Q: Okay, but doesn’t this encourage me to link out less? Should I turn off comments on my blog?

A: I wouldn’t recommend closing comments in an attempt to “hoard” your PageRank. In the same way that Google trusts sites less when they link to spammy sites or bad neighborhoods, parts of our system encourage links to good sites.

I would strongly encourage some testing in this area. Adding links to established page is not the way to go (but by all means try it, much better than taking my word for it). A much better way is to publish a page with embedded links, then pull the links.

Or, publish 10 similar quality articles on related topics in one section of a single website. 5 with curated outbounds, 5 without, and check your aggregate traffic.

********

On the tangent this is heading off on...

Google is now acting the way it always claimed to be acting, by trying to rank sites regardless of SEO. What has happened is people doing what "SEOs" were telling them to do, are now getting punished.

There is some evidence that this has gone slightly too far, in that blatant SEO "tricks" or "worst practices" are getting hit, regardless of the underlying content. But that is an inherent feature in the sensitivity/specificity [en.wikipedia.org] trade-off.

I second the call for testing. I'd do it myself, if Penguin hadn't slaughtered my rankings so completely that it's impossible to develop worthwhile stats from anything I do. I'm making changes to my Penguin-hit heavy outbound link site, but it'll be hard to reach useful conclusions.

I don't doubt you Shaddows, except that if Google did change its algorithm such that outbound links are now important, I would really expect them to trumpet it. I've always wondered why they don't penalize for not linking out. Not linking out doesn't provide their algorithms with the signals they need. I'd expect Google to say "if you link out to quality sites, it can help your rankings" so that they have more data for their algos.

It's just ONE THING, and by itself it means nothing. My sites link out like a mofo, and my rankings never go anywhere but up. I have a couple B2B ecommerce sites under my watch that don't link out at all, and they do fine too. It's just *one thing*.

It's 2012. People need to start looking at forests instead of concentrating on trees.

It's just ONE THING, and by itself it means nothing. My sites link out like a mofo, and my rankings never go anywhere but up. I have a couple B2B ecommerce sites under my watch that don't link out at all, and they do fine too. It's just *one thing*.

It's 2012. People need to start looking at forests instead of concentrating on trees.

And now the tangent is complete.

Of course its one factor. In isolation, everything is just one factor. Writting a paragraph is just one factor. Including an embedded video is just one factor. Including reviews is just one factor. Adding curated outbounds is just one factor.

Also featuring on the list of single factors: - 800x1200 advert on top of page - Adding your keyword to every element, attribute and alt tag you can find - white-on-white text.

So what? Forests are made of trees. You need trees to create a forest.

Can you do well without outbounds? Sure. Do they help? I believe they do.